ANOVA & Bonferroni Correction for Multiple Comparisons: What is Bonferroni’s Correction and When Do We Use It? 👉🏼 ANOVA with R Tutorial: ([ Ссылка ]); ANOVA Complete Video Tutorials ([ Ссылка ]); 👍🏼Best Statistics & R Programming Language Tutorials: ( [ Ссылка ] )

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In this ANOVA video tutorial, we learn about Bonferroni's multiple testing correction (Bonferroni Correction) for Analysis of Variance (ANOVA). When comparing multiple groups, if the null hypothesis is rejected (with a small p-value), the conclusion is that there is evidence that at least one of the means differs from the rest, but there is no indication of which differ from others. To decide which we believe differ, we can conduct "multiple comparisons" of all pairwise sets of means.

While working through an example with multiple comparisons, we will see that because we are making multiple comparisons at once, the chance of making a type I error (false positive) increases. Also called family-wise error rate (FWER), this is the probability of at least one type I error (at least one false positive) when performing multiple hypotheses tests.

Bonferroni proposed a method to correct the inflated type I error rate. Bonferroni assumes that all pairwise tests are independent. This may not be true, but as we will see in this video, independence makes calculations simpler and it is also a bit more conservative. Bonferroni’s approach is to use an adjusted alpha level. The Bonferroni correction sets the significance cut-off for each test at (α/# of tests), in order to have an overall type I error rate of approximately α (alpha).


While Bonferroni's method is not necessarily the `optimal' correction to use, it is easy to understand, and it is conservative. Other methods of correction for multiple comparisons do exist, Tukey's or Dunnett's, for example. They are all based on the same concept, so once you understand Bonferroni's correction, you will be able to understand the concepts behind the other options.

▶︎ The purpose of ANOVA: One Way Analysis of Variance (ANOVA) is used to compare the means of 3 or more independent groups.
▶︎ ANOVA test Assumptions: The ANOVA test requires assuming independent observations, independent groups, that the variance (or standard deviation) of the two groups being compared are approximately equal or that the sample size for each group is large



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▶︎ Analysis Of Variance ANOVA in R, Multiple Comparisons in R, Kruskal Wallis in R [ Ссылка ]
▶︎ANOVA: Use and Assumptions [ Ссылка ]
▶︎ ANOVA: Understanding Sum of Squares [ Ссылка ]
▶︎ ANOVA: Bonferroni Multiple Comparisons Correction [ Ссылка ]
▶︎ Two Sample t test for independent groups [ Ссылка ]
▶︎ Paired t test [ Ссылка ]
► Intro to Statistics Course: [ Ссылка ]
►Data Science with R [ Ссылка ]
►Getting Started with R (Series 1): [ Ссылка ]
►Graphs and Descriptive Statistics in R (Series 2): [ Ссылка ]
►Probability distributions in R (Series 3): [ Ссылка ]
►Bivariate analysis in R (Series 4): [ Ссылка ]
►Linear Regression in R (Series 5): [ Ссылка ]
►Hypothesis Testing: [ Ссылка ]
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Our Team:
Content Creator: Mike Marin (B.Sc., MSc.) Senior Instructor at UBC.
Producer and Creative Manager: Ladan Hamadani (B.Sc., BA., MPH)


These videos are created by #marinstatslectures to support some courses at The University of British Columbia (UBC) (#IntroductoryStatistics and #RVideoTutorials for Health Science Research), although we make all videos available to the everyone everywhere for free.

Thanks for watching! Have fun and remember that statistics is almost as beautiful as a unicorn!

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